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Functional data analysis (FDA) almost always involves smoothing discrete observations into curves, because they are never observed in continuous time and rarely without error. Although smoothing parameters affect the subsequent inference, data-driven methods for selecting these parameters are not well-developed, frustrated by the difficulty of using all the information shared by curves while being computationally efficient. On the one hand, smoothing individual curves in an isolated, albeit sophisticated way, ignores useful signals present in other curves. On the other hand, bandwidth selection by automatic procedures such as cross-validation after pooling all the curves together quickly become computationally unfeasible due to the large number of data points. In this paper we propose a new data-driven, adaptive kernel smoothing, specifically tailored for functional principal components analysis (FPCA) through the derivation of sharp, explicit risk bounds for the eigen-elements. The minimization of these quadratic risk bounds provide refined, yet computationally efficient bandwidth rules for each eigen-element separately. Both common and independent design cases are allowed. Rates of convergence for the adaptive eigen-elements estimators are derived. An extensive simulation study, designed in a versatile manner to closely mimic characteristics of real data sets, support our methodological contribution, which is available for use in the R package FDAdapt.

Arbitrary, inconsistent, or faulty decision-making raises serious concerns, and preventing unfair models is an increasingly important challenge in Machine Learning. Data often reflect past discriminatory behavior, and models trained on such data may reflect bias on sensitive attributes, such as gender, race, or age. One approach to developing fair models is to preprocess the training data to remove the underlying biases while preserving the relevant information, for example, by correcting biased labels. While multiple label noise correction methods are available, the information about their behavior in identifying discrimination is very limited. In this work, we develop an empirical methodology to systematically evaluate the effectiveness of label noise correction techniques in ensuring the fairness of models trained on biased datasets. Our methodology involves manipulating the amount of label noise and can be used with fairness benchmarks but also with standard ML datasets. We apply the methodology to analyze six label noise correction methods according to several fairness metrics on standard OpenML datasets. Our results suggest that the Hybrid Label Noise Correction method achieves the best trade-off between predictive performance and fairness. Clustering-Based Correction can reduce discrimination the most, however, at the cost of lower predictive performance.

Big data streams are grasping increasing attention with the development of modern science and information technology. Due to the incompatibility of limited computer memory to high volume of streaming data, real-time methods without historical data storage is worth investigating. Moreover, outliers may occur with high velocity data streams generating, calling for more robust analysis. Motivated by these concerns, a novel Online Updating Huber Robust Regression algorithm is proposed in this paper. By extracting key features of new data subsets, it obtains a computational efficient online updating estimator without historical data storage. Meanwhile, by integrating Huber regression into the framework, the estimator is robust to contaminated data streams, such as heavy-tailed or heterogeneous distributed ones as well as cases with outliers. Moreover, the proposed online updating estimator is asymptotically equivalent to Oracle estimator obtained by the entire data and has a lower computation complexity. Extensive numerical simulations and a real data analysis are also conducted to evaluate the estimation and calculation efficiency of the proposed method.

Separating signals from an additive mixture may be an unnecessarily hard problem when one is only interested in specific properties of a given signal. In this work, we tackle simpler "statistical component separation" problems that focus on recovering a predefined set of statistical descriptors of a target signal from a noisy mixture. Assuming access to samples of the noise process, we investigate a method devised to match the statistics of the solution candidate corrupted by noise samples with those of the observed mixture. We first analyze the behavior of this method using simple examples with analytically tractable calculations. Then, we apply it in an image denoising context employing 1) wavelet-based descriptors, 2) ConvNet-based descriptors on astrophysics and ImageNet data. In the case of 1), we show that our method better recovers the descriptors of the target data than a standard denoising method in most situations. Additionally, despite not constructed for this purpose, it performs surprisingly well in terms of peak signal-to-noise ratio on full signal reconstruction. In comparison, representation 2) appears less suitable for image denoising. Finally, we extend this method by introducing a diffusive stepwise algorithm which gives a new perspective to the initial method and leads to promising results for image denoising under specific circumstances.

The stochastic dynamic matching problem has recently drawn attention in the stochastic-modeling community due to its numerous applications, ranging from supply-chain management to kidney exchange programs. In this paper, we consider a matching problem in which items of different classes arrive according to independent Poisson processes. Unmatched items are stored in a queue, and compatibility constraints are described by a simple graph on the classes, so that two items can be matched if their classes are neighbors in the graph. We analyze the efficiency of matching policies, not only in terms of system stability, but also in terms of matching rates between different classes. Our results rely on the observation that, under any stable policy, the matching rates satisfy a conservation equation that equates the arrival and departure rates of each item class. Our main contributions are threefold. We first introduce a mapping between the dimension of the solution set of this conservation equation, the structure of the compatibility graph, and the existence of a stable policy. In particular, this allows us to derive a necessary and sufficient stability condition that is verifiable in polynomial time. Secondly, we describe the convex polytope of non-negative solutions of the conservation equation. When this polytope is reduced to a single point, we give a closed-form expression of the solution; in general, we characterize the vertices of this polytope using again the graph structure. Lastly, we show that greedy policies cannot, in general, achieve every point in the polytope. In contrast, non-greedy policies can reach any point of the interior of this polytope, and we give a condition for these policies to also reach the boundary of the polytope.

Recent studies give more attention to the anomaly detection (AD) methods that can leverage a handful of labeled anomalies along with abundant unlabeled data. These existing anomaly-informed AD methods rely on manually predefined score target(s), e.g., prior constant or margin hyperparameter(s), to realize discrimination in anomaly scores between normal and abnormal data. However, such methods would be vulnerable to the existence of anomaly contamination in the unlabeled data, and also lack adaptation to different data scenarios. In this paper, we propose to optimize the anomaly scoring function from the view of score distribution, thus better retaining the diversity and more fine-grained information of input data, especially when the unlabeled data contains anomaly noises in more practical AD scenarios. We design a novel loss function called Overlap loss that minimizes the overlap area between the score distributions of normal and abnormal samples, which no longer depends on prior anomaly score targets and thus acquires adaptability to various datasets. Overlap loss consists of Score Distribution Estimator and Overlap Area Calculation, which are introduced to overcome challenges when estimating arbitrary score distributions, and to ensure the boundness of training loss. As a general loss component, Overlap loss can be effectively integrated into multiple network architectures for constructing AD models. Extensive experimental results indicate that Overlap loss based AD models significantly outperform their state-of-the-art counterparts, and achieve better performance on different types of anomalies.

We study the problem of imputing missing values in a dataset, which has important applications in many domains. The key to missing value imputation is to capture the data distribution with incomplete samples and impute the missing values accordingly. In this paper, by leveraging the fact that any two batches of data with missing values come from the same data distribution, we propose to impute the missing values of two batches of samples by transforming them into a latent space through deep invertible functions and matching them distributionally. To learn the transformations and impute the missing values simultaneously, a simple and well-motivated algorithm is proposed. Our algorithm has fewer hyperparameters to fine-tune and generates high-quality imputations regardless of how missing values are generated. Extensive experiments over a large number of datasets and competing benchmark algorithms show that our method achieves state-of-the-art performance.

In the domain generalization literature, a common objective is to learn representations independent of the domain after conditioning on the class label. We show that this objective is not sufficient: there exist counter-examples where a model fails to generalize to unseen domains even after satisfying class-conditional domain invariance. We formalize this observation through a structural causal model and show the importance of modeling within-class variations for generalization. Specifically, classes contain objects that characterize specific causal features, and domains can be interpreted as interventions on these objects that change non-causal features. We highlight an alternative condition: inputs across domains should have the same representation if they are derived from the same object. Based on this objective, we propose matching-based algorithms when base objects are observed (e.g., through data augmentation) and approximate the objective when objects are not observed (MatchDG). Our simple matching-based algorithms are competitive to prior work on out-of-domain accuracy for rotated MNIST, Fashion-MNIST, PACS, and Chest-Xray datasets. Our method MatchDG also recovers ground-truth object matches: on MNIST and Fashion-MNIST, top-10 matches from MatchDG have over 50% overlap with ground-truth matches.

Data augmentation has been widely used to improve generalizability of machine learning models. However, comparatively little work studies data augmentation for graphs. This is largely due to the complex, non-Euclidean structure of graphs, which limits possible manipulation operations. Augmentation operations commonly used in vision and language have no analogs for graphs. Our work studies graph data augmentation for graph neural networks (GNNs) in the context of improving semi-supervised node-classification. We discuss practical and theoretical motivations, considerations and strategies for graph data augmentation. Our work shows that neural edge predictors can effectively encode class-homophilic structure to promote intra-class edges and demote inter-class edges in given graph structure, and our main contribution introduces the GAug graph data augmentation framework, which leverages these insights to improve performance in GNN-based node classification via edge prediction. Extensive experiments on multiple benchmarks show that augmentation via GAug improves performance across GNN architectures and datasets.

With the explosion of online news, personalized news recommendation becomes increasingly important for online news platforms to help their users find interesting information. Existing news recommendation methods achieve personalization by building accurate news representations from news content and user representations from their direct interactions with news (e.g., click), while ignoring the high-order relatedness between users and news. Here we propose a news recommendation method which can enhance the representation learning of users and news by modeling their relatedness in a graph setting. In our method, users and news are both viewed as nodes in a bipartite graph constructed from historical user click behaviors. For news representations, a transformer architecture is first exploited to build news semantic representations. Then we combine it with the information from neighbor news in the graph via a graph attention network. For user representations, we not only represent users from their historically clicked news, but also attentively incorporate the representations of their neighbor users in the graph. Improved performances on a large-scale real-world dataset validate the effectiveness of our proposed method.